An implicit numerical model for solving free-surface seepage problems

Abstract

ABSTRACT Free-surface seepage problems are one of the most challenging issues in the practice of geotechnical engineering since the determination of the free surface commonly demands sophisticated numerical techniques. This paper introduces an implicit numerical model for determining the free surface of seepage accurately. The present model is based upon the fractional step and finite volume method, which solves the governing equation on an unstructured triangular mesh. In order to reduce the computational complexity and cost, a robust algorithm for solving a system of equations has been presented, which greatly increases the convergence rate. An iterative method has been deployed in an efficient way, through which the non-zero values are extracted from the coefficient matrix of the resultant equation system, whereby the problem unknowns are achieved swiftly. To verify the developed model, several test cases have been utilized. Comparisons between the numerical outcomes, analytical solutions, experimental data, and those of other numerical methods indicate the efficiency and accuracy of the developed scheme and its perfect convergence characteristic. Comparisons between the developed model and other numerical models indicate that the present method is highly robust. The proposed technique provides sufficient accuracy and reliability; besides, it increases the convergence rate through decreasing computational efforts.